An Abstraction of the Unit Interval with Denominators

Speaker: Marco Abbadini

Wednesday, 4 January 2023, 14:00, visio link:

Abstract: Compact Hausdorff spaces are the topological abstraction of the unit interval [0,1] (in a sense that can be made precise). Let us now equip the unit interval with the "denominator map" den: [0,1] -> N that maps a rational number to its denominator and an irrational number to 0. We characterize the abstraction of [0,1] that takes into account both the topology and the denominator map.

(We use this result to provide a representation theorem for a class of lattice-ordered groups, generalizing a result of M.H. Stone (1941).)